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arXiv · 1203.3222

A note on monomials

J. M. Almira·Kh. F. Abu-Helaiel
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Abstract

We study discontinuous solutions of the monomial equation $\frac{1}{n!}\Delta_h^nf(x)=f(h)$. In particular, we characterize the closure of their graph, $\bar{G(f)}^{\mathbb{R}^2}$, and we use the properties of these functions to present a new proof of the Darboux type theorem for polynomials and of Hamel's theorem for additive functions.

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J. M. Almira, Kh. F. Abu-Helaiel. 2012-03-14. A note on monomials. https://arxiv.org/abs/1203.3222

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